熱電元件能將熱與電進行轉換，主要用於廢熱回收和固態冷卻等應用。廢熱回收能提高能源使用效率，因此熱電材料與元件吸引了非常多的關注與探討。Bi-Sb-Se-Te是重要的四元材料系統，此系統中包括Bi2Te3,、Sb2Te3、Bi2Se3、Sb2Se3、(Bi,Sb)2Te3、Bi2(Se,Te)3、(Bi,Sb)2Se3、Sb2(Se,Te)3及(Bi,Sb)2(Se,Te)3等多種化合物都是重要的熱電材料。相圖是表達材料相平衡最簡潔的方法，是材料的重要基礎知識，對新材料的研發及製備很有助益。本研究探討Bi-Sb-Se-Te四元材料系統相平衡，以實驗量測與CalPhad計算的方法來建構此系統的相圖。
相平衡量測實驗是將純Bi、Sb、Se與Te元素依不同比例製備成合金試樣後，將其熔融均勻並置於高溫爐中一段時間以達熱力學平衡。接著取出淬冷於水中後進行金相、相組成與粉末X-光繞射分析，以了解其平衡相的資訊。利用實驗所得平衡相資訊與相關的文獻資料，再以符合熱力學的規律，推導出等溫橫截面相圖。在液相線投影圖的測定中，則是利用熔融均勻後的試樣直接進行固化，觀測其首要析出相與熱分析實驗所得的相變化溫度來制定的。當中首要析出相的分析同相平衡量測實驗，需利用金相、組成與X-光繞射分析來測定。熱力學模型的建立與相圖計算，則採用CalPhad的方法與商用計算軟體Pandat。
此四元系統有六個二元子系統，Bi-Sb、Bi-Se、Bi-Te、Sb-Se、Sb-Te和Se-Te，與四個三元子系統，Bi-Sb-Se、Bi-Sb-Te、Bi-Se-Te和Sb-Se-Te。有關於二元系統的文獻資料較完善，本研究從眾多文獻中評估，挑選出最適切的二元系統相圖與Calphad的熱力學模型。三元系統的相平衡資料較少，經過評估，文獻中已有可靠的Bi-Se-Te與Sb-Se-Te三元系統相平衡資料與相圖。在本研究中以實驗與計算的方法測定Bi-Sb-Se與Bi-Se-Te的三元系統相圖，並依據三元系統的相圖以及本研究實驗所測定的Bi2Se3-Sb2Se3-Bi2Te3-Sb2Te3於400oC等溫截面圖，建立了Bi-Se-Se-Te在400oC等溫四面體相圖。
液相線投影圖的投影線代表著單一變數線(univariant line)，也區隔著不同的首要析出相。在本研究實驗結果，發現Bi-Sb-Se三元系統中有七個首要析出相區，包含(Bi,Sb)、(Bi2)m(Bi2Se3)n、Bi2Se3、Se、Sb2Se3及本研究新發現的Bi3Sb5Se2以及Bi3Sb12Se5三元相。由於在本研究中難以區分兩三元相，故以Bi30-xSb55Sex相代表此兩相。從溫度與生成相的組成，推知Bi-Sb-Se三元系統具有五個不變反應(invariant reaction)。分別為: Liquid+Sb2Se3+Bi2Se3=Se (ClassШ)、Liquid+Bi2Se3=Sb2Se3+ (Bi2)m(Bi2Se3)n (ClassⅡ)、Liquid+Sb2Se3+ (Bi,Sb)= Bi30-xSb55Sex (ClassШ)、Liquid+Sb2Se3+Bi30-xSb55Sex =(Bi2)m(Bi2Se3)n (ClassШ)、Liquid+Bi30-xSb55Sex =(Bi,Sb)+(Bi2)m(Bi2Se3)n (ClassⅡ)。經由熱分析的方式測得兩個不變反應溫度: Liquid+Sb2Se3+(Bi,Sb)= Bi30-xSb55Sex，反應溫度為520oC; Liquid+Bi2Se3 =Sb2Se3+ (Bi2)m(Bi2Se3)n，反應溫度為580oC。
本研究發現在Bi-Sb-Se 400oC有兩個三元相的存在:Bi3Sb5Se2以及Bi3Sb12Se5，並發現Sb對於(Bi2)m(Bi2Se3)n的溶解度高達38at.%。依據相關二元與三元系統的相平衡資料，Bi-Sb-Se在400oC具有8個單相: Bi2Se3、Sb2Se3、Bi3Sb5Se2、Bi3Sb12Se5、(Bi,Sb)、(Bi2)m(Bi2Se3)n、Liquid(Bi)以及Liquid(Se)。並有15個兩相區以及8個三相區。
在Bi-Sb-Se 相圖計算中，統整了文獻中對於三個二元子系統的熱力學參數，並根據本實驗的研究成果引入三元系統參數進行熱力學模型的修改。目前計算預測於400oC的熱力學平衡相與本研究所制定的相當接近。
在Bi-Se-Te 400oC等溫橫截面圖系統中並未發現三元相的存在。並發現(Bi2)m(Bi2Se3)n以及(Bi2)m(Bi2Te3)n可形成一同質互溶體(Bi2)m(Bi2(Se,Te)3)n。依據相關二元與三元系統的相平衡資料以及本研究成果，Bi-Se-Te在400oC下具有5個單相: Bi2(Se,Te)3、Liquid(Se,Te)、Solid(Se,Te)、Liquid(Bi)、(Bi2)m(Bi2(Se,Te)3)n，5個兩相區以及1個三相區。
在Bi-Se-Te相圖計算中，統整了文獻中對於三個二元子系統的熱力學參數，並根據本實驗的研究成果引入三元系統參數進行熱力學模型的修改。目前計算預測的結果與本研究以實驗制定的接近。
在Bi-Sb-Se-Te四元系統相圖，針對Bi2Se3-Sb2Se3-Bi2Te3-Sb2Te3的等溫橫截面區域進行金相結構的觀測，發現在(Bix,Sb1-x)2(Sey,Te1-y)3組成下的大部分區域呈現均一相，並有相似的晶體結構。

Thermoelectric devices can improve energy usage efficiency by converting waste heat to electricity. They are mainly used in application such as waste heat recovery and cooling device. Therfore, thermoelectric materials and devices have attracted a lot of attention and discussion. Bi-Sb-Se-Te quaternary system is an important thermoelectric material system. It has various compounds of promising thermoelectric properties, including Bi2Te3, Sb2Te3, Bi2Se3, Sb2Se3, (Bi,Sb)2Te3, Bi2(Se,Te)3, (Bi,Sb)2Se3, Sb2(Se,Te)3, and (Bi,Sb)2(Se,Te)3, etc. Phase diagrams contain phase equilibria information which is fundamentally important for materials design and processing. This study determines the phase diagrams of Bi-Sb-Se-Te quaternary system and its constituent sub-systems by both experimental measurements and Calphad-type calculation.
For phase equilibria measurements. Quaternary Bi-Sb-Se-Te alloys are prepared with pure constituent elements and equilibrated at 400oC. Their equilibrium phases are determined based on the results of metallographical, compositional and XRD analysis. The phase diagrams are constructed based on the determined phase equilibria results and related phase diagrams from the literatures. The liquidus projection is constructed by thermal analysis and the study of primary solidification phase. The phase transformation temperature is measured by thermal analysis and the primary solidification phases are determined from the as-quenched alloys. For the construction of thermodynamic model, it is determined by the Calphad method and Pandat software developd by Computherm.
Bi-Sb-Se-Te quaternary system contains six constituent binary systems and four constituent ternary systems, including Bi-Sb, Bi-Se, Bi-Te, Sb-Se, Sb-Te, Se-Te,. Bi-Sb-Se, Bi-Sb-Te, Bi-Se-Te, and Sb-Se-Te. The information of the binary systems is relative complete in literatures. The most appropriate binary system phase diagram and thermodynamic model are selected from literatures in this study. For ternary systems, Bi-Se-Te and Sb-Se-Te ternaty system phase equilibria data and phase diagrams are relatively complete in the literatures. In this study, the ternary phase diagram of Bi-Sb-Se and Bi-Se-Te are determined by both experimental measurements and Calphad-type calculation. Bi-Sb-Se-Te 400oC isothermal section is determined based on the the isothermal section of Bi2Se3-Sb2Se3-Bi2Te3-Sb2Te3 and the four constituent ternary systems in this study.
In this study, we determine the univariant line from different primary solidification phases. Seven primary solidification phases are observed in Bi-Sb-Se liquidus projection. Including (Bi,Sb), (Bi2)m(Bi2Se3)n, Bi2Se3, Se, Sb2Se3, Bi3Sb5Se2, and Bi3Sb12Se5 phases. However, Bi3Sb5Se2 and Bi3Sb12Se5 phases are difficult to distinguish in this stidy. These two phases’ region is represented by Bi30-xSb55Sex. Accroding to the phase transformation temperature and precipitation order of phases, there are five invariant reactions, Liquid+Sb2Se3+Bi2Se3=Se (ClassШ), Liquid+Bi2Se3=Sb2Se3+(Bi2)m(Bi2Se3)n (ClassⅡ), Liquid+Sb2Se3 +(Bi,Sb)=Bi30-xSb55Sex (ClassШ), Liquid+Sb2Se3+Bi30-xSb55Sex=(Bi2)m(Bi2Se3)n (ClassШ), Liquid+Bi30-xSb55Sex =(Bi,Sb)+(Bi2)m(Bi2Se3)n (ClassⅡ).
Two invariant reaction temperature are found by thermal analysis in this study. Liquid+Sb2Se3+Bi30-xSb55Sex=(Bi2)m(Bi2Se3)n (ClassШ) at 520oC and Liquid+Bi2Se3= Sb2Se3+(Bi2)m(Bi2Se3)n (ClassⅡ) at 580oC.
Two ternary compounds, Bi3Sb5Se2 and Bi3Sb12Se5, are found in Bi-Sb-Se 400oC isothermal section. The solubility of Sb in (Bi2)m(Bi2Se3)n is 38at.%. Accroding to the relation information of phase diagram for this system. There are eight single-phase regions in this system, Bi2Se3, Sb2Se3, Bi3Sb5Se2, Bi3Sb12Se5, (Bi,Sb), (Bi2)m(Bi2Se3)n, Liquid(Bi), and Liquid(Se).
The calculation result of Bi-Sb-Se system is determined based on the three constituent binary systems from literatures and the experiment results in this study. In most case, the calculation result is in agreement with the experiment results.
Bi-Se-Te 400oC isothermal section is determined in this study. No ternary compounds are found in this system. The (Bi2)m(Bi2Se3)n and (Bi2)m(Bi2Te3)n form continuous solid solution (Bi2)m(Bi2(Se,Te)3)n. Accroding to the relation information of phase diagram for this system. There are five single-phase regions, Bi2(Se,Te)3, Liquid(Se,Te), Solid(Se,Te), Liquid(Bi), and (Bi2)m(Bi2(Se,Te)3)n in this system.
The calculation result of Bi-Se-Te system is determined based on the three constituent binary systems from literatures and the experiment results in this study. The calculation result shows in agreement with the experiment results in this study.
In Bi-Sb-Se-Te quaternary system, the experiment results show a wide single phase region in Bi2Se3-Sb2Se3-Bi2Te3-Sb2Te3 isothermal section.

摘要 ii
Abstract v
目錄 viii
圖目錄 xi
表目錄 xxii
1. 前言 1
2. 文獻回顧 5
2-1 相圖 5
2-1-1 實驗建立相圖 7
2-1-2 計算建立相圖 8
2-2 二元系統回顧 9
2-2-1 Bi-Sb二元系統相平衡 9
2-2-2 Bi-Se二元系統相平衡 10
2-2-3 Bi-Te二元系統相平衡 13
2-2-4 Sb-Se二元系統相平衡 17
2-2-5 Sb-Te二元系統相平衡 20
2-2-6 Se-Te二元系統相平衡 23
2-3 三元系統回顧 25
2-3-1 Bi-Sb-Se三元系統相平衡 25
2-3-2 Bi-Sb-Te三元系統相平衡 27
2-3-3 Bi-Se-Te三元系統相平衡 30
2-3-4 Sb-Se-Te三元系統相平衡 33
3. 研究方法 35
3-1 金相實驗 35
3-2 相圖計算 38
4. 結果與討論 41
4-1 Bi-Sb-Se 液相線投影圖研究方法 41
4-1-1 (Bi,Sb)首要析出相區: 50
4-1-2 (Bi2)m(Bi2Se3)n首要析出相區 61
4-1-3 Bi2Se3 primary solidification phase section 71
4-1-4 Bi30-xSb55Sex primary solidification phase section 77
4-1-5 Sb2Se3 primary solidification phase section 84
4-1-6 Bi-Sb-Se三元系統熱分析 94
4-1-7 Bi-Sb-Se統整液相線投影圖 100
4-2 Bi-Sb-Se於400oC下的等溫橫截面圖 102
4-2-1 Bi2Se3+Sb2Se3+Se三相區 108
4-2-2 Bi2Se3+Sb2Se3+(Bi2)m(Bi2Se3)n三相區 110
4-2-3 Bi3Sb5Se2+Bi3Sb12Se5+(Bi,Sb)三相區 111
4-2-4 Bi3Sb5Se2+(Bi,Sb)+Liquid(Bi,Sb)三相區 114
4-2-5 Bi3Sb5Se2+(Bi2)m(Bi2Se3)n +Sb2Se3三相區 116
4-2-6 (Bi2)m(Bi2Se3)n +Bi2Se3兩相區 118
4-2-7 Bi3Sb12Se5+(Bi,Sb)兩相區 120
4-2-8 Bi3Sb12Se5+ Sb2Se3兩相區 124
4-2-9 Bi3Sb5Se2+Liquid兩相區 127
4-2-10 (Bi2)m(Bi2Se3)n +Sb2Se3兩相區 130
4-2-11 (Bi2)m(Bi2Se3)n +Liquid兩相區 132
4-2-12 Bi2Se3+Sb2Se3兩相區 137
4-2-13 (Bi2)m(Bi2Se3)n單相區 138
4-2-14 Bi3Sb5Se2單相區 141
4-2-15 Bi-Sb-Se於400oC下的等溫橫截面圖 143
4-3 Bi-Sb-Se 計算相圖 145
4-4 Bi-Se-Te 於400oC下的等溫橫截面圖 154
4-4-1 (Bi2)m(Bi2(Se,Te)3)n 單相區 158
4-4-2 (Bi2)m(Bi2(Se,Te)3)n+Liquid(Bi)兩相區 163
4-4-3 Bi2(Se,Te)3+Liquid(Se,Te)兩相區 165
4-4-4 (Bi2)m(Bi2(Se,Te)3)n+Bi2(Se,Te)3兩相區 168
4-4-5 Bi2(Se,Te)3+Solid(Se,Te)兩相區 170
4-4-6 (Bi2)m(Bi2(Se,Te)3)n+Liquid(Se,Te)+Solid(Se,Te)三相區 174
4-4-7 Bi-Se-Te於400oC下的等溫橫截面圖 178
4-5 Bi-Se-Te計算相圖 180
4-6 Sb-Se-Te於400oC下的等溫橫截面圖 188
4-6-1 Sb2Se3+Solid(Se,Te)兩相區 191
4-6-2 Sb2Se3+Sb2Te3+Solid(Se,Te)三相區 194
4-6-3 Sb2Te3+δ-(Sb2Te)兩相區 197
4-6-4 δ-(Sb2Te)+γ-(SbTe)兩相區 199
4-6-5 Sb2Te3單相區 200
4-6-6 Sb2Se3+δ-(Sb2Te)+γ-(SbTe)三相區 201
4-6-7 Sb-Se-Te於400oC下的等溫橫截面圖 203
4-7 Bi2Se3-Sb2Se3-Bi2Te3-Sb2Te3 於400oC下的等溫橫截面圖 205
4-7-1 (Bi,Sb)2(Se,Te)3單相區: 208
4-7-2 Sb2Se3-(Bi,Sb)2(Se,Te)3兩相區 216
4-7-3 Bi2Se3-Sb2Se3-Bi2Te3-Sb2Te3於400oC等溫橫截面相圖 217
4-7-4 Bi-Sb-Se-Te於400oC等溫立體相圖 218
5. 研究成果 219
6. 參考文獻 221

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